Gibbs measures for fibred systems

Manfred Denker, Mikhail Gordin

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


We consider a topological dynamical system T:Y→Y on a metric space Y which forms a fibre bundle over another dynamical system. If T is fibrewise expanding and exact along fibres and if φ is a Hölder continuous function we prove the existence of a system of conditional measures (called a family of Gibbs measures) where the Jacobian is determined by φ. This theorem reduces to Ruelle's Perron-Frobenius theorem when the base of the fibred system consists of a single point. The method of proof does not use any form of symbolic representation. We also study continuity properties of a family of Gibbs measures (over the base) and give applications to the equilibrium theory of higher dimensional complex dynamics.

Original languageEnglish (US)
Pages (from-to)161-192
Number of pages32
JournalAdvances in Mathematics
Issue number2
StatePublished - Dec 25 1999

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


Dive into the research topics of 'Gibbs measures for fibred systems'. Together they form a unique fingerprint.

Cite this